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Dec. 25, 1956 E. wr-:lss 2,775,402

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CODED DECIMAL SUMMER Filed May 25, 1951 7 Sheets-Sheetl 5 @ff f @@,gp 654;) Kef-2) f2 @wfg f) t (5 F29; .1L L 5J gf-4 Filed May 25, 1951 @14 7 Sheets-Sheet 6 Dec. 25, 1956 E WEls 2,775,402

` coDED DECIMAL SUMMER,

United States Patent O CODED DECIMAL SUMMER Eric Weiss, Los Angeles, Calif.

Application May 25, 1951, Serial No. 228,235

12 Claims. (Cl. 23S-61) The present invention relates to electronic digital adding circuits and more particularly to a novel adding means and method for operating on numbers expressed by a coded decimal system.

It is well known that digital computers can be devised using bistable state devices, such as flip-flops, for` manipulating'binary representations of numbers. Because e of the simplicity of the binary numbers, i. e., either a 1 or a 0, the means for operating on the digits is comparatively less complex than for other number systems. I

absence or presence of binary digit ones in each of the i four digit positions within this block, -the magnitude of the decimal digit is determined. t

It is accordingly an object of this invention to provide an electronic means and method for receiving two numbers represented in a coded decimal system and emitting their sum represented in the same coded decimal system.

It is another object of this invention to provide a novel electronic means and method for lsumming two coded decimal numbers using a storage means that can be efficiently used for storing different types of information as needed during the operation.

It is another objectof this invention to provide a novel electronic means and method for summing two coded numbers having a minimum delay between the inputs and the outputs.

It is still another object of this invention to provide a novel counting circuitrywhich can record a binary count by increasing its content from any given value in accordance with the weight given to a pair of incoming digits by a given code. t t

It is still another object of this invention to provide a novel binary coded system for representing decimal numbers which can be operated upon with all the `features of advantage usually associated with straight binary number systems. l

Brieily, the summing circuit of the present invention is comprised of bistable state devices, such as flip-flop circuits, and an associated control network. The two waveform patterns representing the numbers to be summed are serially fed into the control network which has a cycling action controlled by clock pulse inputs fed in from another source.- The single output waveform pattern from the summer represents the number corresponding to the sum of the input pulse numbers and is indicated by the same code used for expressing the inputs.

The control network for the flip-flops operates according to a set of logical equations. Each of the equations 2,775,402 'Patented Dec. 25, 1956 ICC defines when and how a nip-flop will change its state. The outputs of the flip-flops, together with the input waveforms, represent the yterms of the equations which are combined by logical multiplication or logical addition operations These operations are physically performed by networks comprising arrangements of diodes and resistors which interconnect the lines carrying the voltages representative of the terms The clock pulses are used for synchronizing and beating the summing circuit. Whenever, as the result of a clock pulse actuation, the terms of the network are made proper to satisfy a control input to a flip-flop, the logical multiplication of this control input with the next clocky pulse causes the flip-op to change, unless it is already in the state controlled by the input, in which event it remains in that state.

The cycling action of the summer circuit corresponds to the receipt of four successive binary digits which define .a decimal block. An auxiliaryset of ip-flops is arranged to successively count clock pulses and emit potentials representative of the four cycle counts.

Thus, it can be stated that the electrical status of the logical network, and consequently the flip-ilops themselves, change in response to voltages (terms) representing: digit inputs, the states of the flip-flops following the previous clock pulse actuation, and the step of the cycle through t which the summer advances.

The invention will be more clearly understood by the following detailed description of a preferred form of the invention taken together with the accompanying drawings forming a part of this specication in which:

Figure l is a schematic block diagram showing generally the arrangement of the preferred embodiment of the summer circuit.

Figure 2 is a binary table showing the four place code representing each of the decimal digits.

Figure 3 is a block diagram of the cycle counter together with the logical equations defining the triggering inputs for each of the ip-flop stages.

Figure 4 is a binary table showing the states of the F flip-flops characteristic of the cycle count.

Figure 5 is a detailed circuit diagram of the F1 flipflop in the cycle counter.

Figure 6 is a graph of the voltage waveforms which are referred to in explaining the operation of the F1 flipop. t

Figure 7 is a schematic circuit diagram of the counting logical net for the cycle counter.

Figure 8 is a binary table showing the decimal equivalent of the binary contents of the hip-flops comprising the summer. Y

Figure 9 is a block diagram of the summer flip-flops 'together with Ithe symbolic equations defining the grid triggering inputs.

Figure 10 is a diode net for generating complex propositions which are used a plurality of times in the logical diode nets.

Figures 11 and l2 are schematic circuit diagrams of the grid input logical nets for the S1 Hip-flop.

Figure 13 is a schematic circuit diagram of the grid input logical nets for the S2 hip-flop.

Figures 14 and 15 are schematic circuit diagrams of the grid input logical nets for the. S3 flip-op.

Figures 16 and 17 are schematic circuit diagrams of the grid input logical nets for the S4 flip-flop.

Figure 18 is a schematic circuit diagram of the output logical nets for generating the voltage waveform representing the sum.

Referring rst to Figure l, a block diagram shows the general arrangement of the present invention. The summer lil is comprised of ip-ops S1, S2, S3, and S4 Itogether with an arithmetical and output logical net 11. The potential waveforms appearing on inputs Sa and Sb The flip-nop circuit as usedin the present invention is well known in that it is comprised of two triodes, Viand V2, having opposite plates and grids intercoupled by a resistor R in parallel with a capacitor C. The plate of each of the triodes is connected through a separate load resistor, like resistor R1, to a positive D. C. source B+, and the cathode of each triode is grounded. Each of the grids of the tubes is joined through a separate grid resistor R2 to a negative bias -E. The flip-flop circuit is provided with triggering circuits associated with each of its grids and output circuits connected to each of its plates.

Whenever the flip-flop is considered to be in a one state, neon light L, connected in series with a limiting resistor Ro across the left load resistor R1, lights up; and when the flip-flop is in a zero state, neon light L is out.

The output lines F1 and F1 from the F1 hip-flop are 'taken from the right and left plates respectively. In order to maintain the swing of the plate voltage between voltage levels Eh and E1, clamping diodes, such as diodes 20 and 21 associated with the right output Fi, are provided on each of the output lines.

The inputs to the ilip-op are controlled by gate circuits 22 and 23 associated with the grids of the V1 and V2 tubes, respectively. Each of the gates is coupled through a differentiating circuit 24 and blocking diode 25 as shown in particular for the left grid, the grid of tube V1.

For this particular. counting stage, the right plate output F1 is connected to one input of the lef-t gate 22, and the left plate output F1 is connected to one input of the right gate circuit 23. The clock pulse C is applied simultaneously to the second inputs of `each of the left and right gate circuits 22 and 23.

These gate circuits 22 and 23 are typical logical product diode nets. In such a circuit, as noted in particular for left gate 22, the inputs therein are applied on the cathodeends of crystal diodes 27 and 28 whose anode-ends are joined to a common line 29 which is connected to a positive source B-l- `through a load resistor R3.

Any time the plate input to Ithe gate circuit is high in potential, the clock pulse C applied to fthe other input 1s, in effect, passed to the output. This pulse is differentiated in differentiating circuit 24 and the positive portion thereof is blocked by diode 25 while the negative portion is passed therethrough and thus triggers the V1 tube oil.

In Figure 6 the graphs of the waveforms appearing at different points of the F1 counting stage circuit, above described, are shown. In line I the regularly recurring clock pulses C are shown; in line. II the Fi plate output is shown to be initially of a high voltage (Eh); while in line III the F1' plate output .is lshown to be initially of a low voltage (E1). As shown 1n line 1V, whenever both the waveforms Fi and C are relatively high in potential, the term ofi is considered to pass through the gating circuit 22 as a rectangular pulse similar in waveform to the clock pulse C. The clock pulse source is of very low impedance so as to ensure that the trailing edge of the wave is not rounded but relatively square. On line V, the pulse form impressed on the input to the left grid is shown to be essentially the differentiated trailing edge 31 ofV the rectangular pulse ofi. It is thus noted that the F1 flip-Hop changes state on the trailing edge of the ofi pulse (clock pulse C). It is also noted that as a result of triggering the left tube V1 ott, the left plate output Fi rises in potential according to the time constant of the flip-hop circuit. The output Fi is now high in potential so that on occurrence of the next clock pulse C, the lright gate 23, in effect, allows the clock pulse C to pass therethrough and hence the differentiated trailing edge 32 of this latter pulse triggers the F1 flip-flop back toits original state. Y

It is now'evident that the clock pulse period divides the timing of the circuit operations into three distinct steps. During the first part of a clock pulse period, when the voltage from the clock source is low, the

transients of the circuitry areoccurring. For reliability,-

theseshould befcompleted before the leading' edge of the clock pulse arrives. During the time of the clock pulse the logical net circuits can be thought of as observing' the Hip-flops and the other sources of inputs so as to know if a pulse should pass onto the grid of any of the flip-flops. The clock pulse must be broad enough so that, taking into account its rise time, it reaches its maximum voltage level before the end of the clock period. The clock pulse must also have a low impedance source, so that a square edge can be created on the trailing end of the pulse passing through the grid gates. These conditions make it possible to create by differentiation, a negative pulse, coincident with the end ofthe clock period, which can be used for triggering the flip-flops.

Referring next to Figures 3 and 7 the simplified manner in which the remaining circuitry of the present invention is to be presented will now be described.

Instead of showing the wiring diagrams of the flipflops together with the logical circuits, as in Figure 5, the remaining circuits present simplified block diagrams of the flip-flops. It should be understood however, that all the ip-tlop circuits are identical. As shown in Figure 3, only the input and output lines for the ip-op are indicated and these are marked in accordance with the convention previously described. Furthermore, the grid input differentiating and `blocking circuits are omitted in the block diagrams for simplicity. Only the gates, indicating the logical product of the control input and clock input, are shown at each of the inputs so as to emphasize the fact that the clock pulses are applied simultaneously to all the flip-flop inputs.

ln accordance with the scheme of the present invention, after the system of thought to be accomplished is explained by means of binary tables or similar means for systematizing the thought, the terms ofthe system are represented by the conditions of flip-flop circuits, or other sources of potentials having two possible levels.

Logical equations are then Written which dene when and how the ip-flop circuits are to change in accordance with the eiective terms of the system. The logical equations, so devised, are then presented below the block diagram of the ilip-ilops.

Writing the logical equations for the grid triggering of a flipflop circuit is no more than stating the terms which have to be simultaneously of a high potential in order that the particular flip-Hop should trigger into the particular state. Two distinct notations are used for the equations. The rst, logical multiplication means that all the terms in the particular product have tobe of high potential in order to make that product effective in a particular equation. The second, logical addition means that at least one term of the sum has to be of high potential in order to make that sum effective in a particular equation.

Thus, for-example, the equation means that the S3 flip-flop will change to the false state after the following four terms are at a high potential: Ss, (S14-S2), C, P4 where the term (Si-l-Sz), itself, will be of high potential if either Si is of high potential, or S2, or both.

The particular representation of these logical equations v equations to physical circuitry, recognition is made of the fact that certain common complex terms and partial products can be generated separately and` used repeatedly where needed. This results in a reduction of the number of components required but ofteneat thefexpense of complicating the recognition of the original'equations. The present techniques, however, make it possible to retain in the equations the original system of thought, even though the equations go through several-revisions, as long as the revisions are according to the well known rules of symbolic logic.

It should be noted that circuits to solve logical multiplication are also called gates, and circuits to solve logical addition 'are also called mixers Returning back to Figure 3, the conditions required for flipping the F1 flip-flop, as previously described Yin connection with Figure 5, are representedA by symbolic logic equations f1=F 1C and nf1=F1C.

By examining the states of the F flip-flops, as presented in Figure 4, the symbolic logic equations for the F2 ipflop can be similarly determined. The conditions necessary to make ip-op F2 trigger to a true state, i. e., change from a to a 1 state, are that flip-flop F1 be ina true state and flip-flop F2, itself, be in a false state; this can be symbolically noted by f2=F2F1C. In a similar manner, the conditions required to make the flip-flop F2 false are that flip-op F2 be true `and llip-op'Fl be true, i. e. of2=F2F1C.

The logical diode nets used for physically solving all the triggering equations for the F counter are next introduced in Figure 7.

The nets for the equations uf1=F1C and f1=F1C for the F1 flip-flop are the gate circuits 22 and 23, respectively, shown in Figure 5. Here they are simply shown by designating the inputs to the gate 22, known as the typical two input product gate, by terms of the ofi equation; and by designating the inputs to the product gate 23 by terms of the f1 equation. The outputs of these gates are marked respectively ofi and f1. Each of these product circuits is such that whenever any of the inputs are of relatively low potential, the output is also of relatively low potential; however, when all the inputs are of relatively high potential, the output is also of relatively high potential. In other words, the output potential equals the lowest input potential.

The equation for gate f2 is seen, in Figure3, to be a product of the same two terms defining 0f1 multiplied by an additional term F2'. It should be noted in Figure 7 that instead of providing a three input product circuit for solving the f2 equation, the output of the two input product circuit 22 is cascaded into a second two input product circuit 4t) along with the new term F2'. Thus the output f2 of the 'second two input product circuit 40 generates the f2 solution.

The equation @f2 also includes the common product dening ofi. Hence the outputs of the two input product circuit 22 is also fed as one of the inputs 41'into a third two input product circuit 42 along with the new term F2. The output of this third product circuit 42 provides ofz.

The above circuits illustrate clearly how the equations for the input to the proposition dip-flops operate as a key, revealing the manner in which the outputs of the flip-flops are logically interconnected to the inputs, i. e., they dene how 'and when the flip-flops should change with respect to the conditions of other propositions in the circuits.

The equation representing the timing pulses P1, P2, P3 and P4 are seen in Figure 4 to be composed of logical products of the terms represented by the outputs from the F flip-flops. These products are physically generated by the networks shown in Figure l0. Here it is shown that P1=F1F2 is manifested on line 44, Pz=F1F2 on line 65 Pa=F1F2 on line 66 and P4=F1F2 on line 67.

Returning again to Figure l, the summer circuit 'will now be described in detail.

The summer hip-flops fundamentally function as a 8 straight binary counter, that is, the S1 flip-Hop represents the 2k stage, and the S2, S3, and S4 ilip-flops-represent the21, 22 and 23 stages, respectively, ofthe counter.

However, although the S counter flip-flops manifest a binary count, the binary digit l inputs to the S counter do not always represent unit weight, but, depending on the cycle pulse time, may also be weighted either two or five units. Another feature of the S counter is that it must be able to handle inputs from two sources Sa and Sb. Still another feature of the counter is that there must be complete generality in counting so that the counter can increase its count from any given count, within certain dened limits, in accordance with the weight of the inputs received.

Referring next to Figure 9, the schematic block diagrams of the S1, S2, S3, and S4 flip-flops are shown together with the trigger logical equations associated with each of the grid inputs.

During the P1 and Pzpulse times (Figure 2), the effective external inputs (high potentials) received on Sa and Sb are given unit weight in the S counter, that is, the counter flip-flops function as a unit counter.

It should be noted that the range of KA, the content of thev counter for P1 time, is OSKASS. That is to say, any number of unit inputs from 0 to 3 may be received. It is when aunit carry is received from aprevious addition, simultaneously with a unit input on Se. and Sb, that the counter can record a content of 3.

Referring to Figure 8, a binary table shows the states of the S flip-flops equivalent to the decimal counts. The S flip-ilops are here noted to indicate a binary count in la conventional manner. The range KA of the counter is seen to include flip-flops S1 and S2 so that as far as counting is concerned only these flip-Hops need be taken into account during P1 time.

On this basis, theequations for the S1 flip-flop during P1 time are determined to be as follows:

These equations, in effect, indicate that if a unit is fed into the counter. from either of the two external inputs S1. or Sb, but not both; if the S1 flip-flop is in the 0 state it will flip to the l state, and if it is in the l state it will flip to the 0 state. This mode of operation is in accord with the binary counting table shown in Figure 8 which indicates that as unit inputs are added to the counter, the S1 flip-flop records the change by iiipping to the opposite state from which it was in before the unit input.

Since, as indicated, the maximum count (decimal) which can be stored in the counter during P1 time is 3, it is possible that the S2 flip-flop may be triggered to a 1 state but never to a 0 state. Thus the input equations to fthe S2 flip-flop need only be written for sz, the input which renders the S2 flip-flop true, the other input being necessarily equal to zero, thus:

Equation s2 indicates that whenever a count of at least two inputs is indicated during the P1 time, whether by units on each of the external inputs or a unit on one of the external inputs and a one content already in the S1 Hip-flop, the S2 flip-flop records a one on the next clock pu se.

It is to be noted by equation nsa=CP1, that the S3 ipiop is set false at the end of the P1 pulse time. The reason for this is that during P1 time the weight 2 component, stored (at the end of P4 time) as a result of the previous coded decimal sum cycle, is read out of the S3 flip-flop. As will be made more evident in the ensuing discussion the S3 dip-flop was used for storing a coded binary output digit during the P1 time. Clearing the S3 flip-flop makes it possible to` again utilize this flip-flop as a counting stage as required during P2 and Ps times.

This is brought out by the table in Figure 8 which shows that during the P2 pulse time, the totalcount of the units, KB, has the range C Ks Note that during P1 time the maximum count may be 3 and by adding a unit on each of the external inputs during the Pz time, this total may be as great as 5. Thus it requires ipilops S1, S2, and S3 to store the magnitude Kn and hence equations must be written for all these ip-op grid inputs.

The equations for the S1 Hip-op during the Pz pulse time are:

These equations are identical to the S1 ip-lop equations for the P1 pulse time in that they provide for increasing the content of the counter by one unit when only one of the external inputs, Sa or Sb, indicates a one.

As for the S2 hip-flop, during the P2 pulse time, the inputs are as follows:

Note that the true grid input equation s2 functions the same as for the P1 time. The usz equation is herein introduced to change ip-ilop S2 to a zero or false state as is needed when the units received, plus the previous contents of the counter, total 4 (or 5). As seen in Figure 8, 4the count 4 (or 5) is evidenced by a zero in the S2 flipflop.

In order to record a 4 (or 5) in the counter during P1 time, by the same reasoning which is used for setting flipilop S2 alse,the S3 ilip-op must be set true. Thus:

The reason the usa equation is set equal to zero is because the maximum count which can be stored 'in the counter during P2 time is 5, and, as seen in Figure 8, to record this count, the S3 ip-flop may have to be triggered to a true state, but never back to a false state.

It should be noted that following the Pz time the S4 iiip-lop` is reset to zero by equation The purpose for this is similar to the reason the S3 flip-flop was reset during the P1 time. In this case the S4 flip-flop was storing the 5 weight component of the decimal digit output representing the sum of the previous cycle operation. This component, having been read out during the P2 time, is no longer needed.

The grid input equations for the S counter ip-flops will now be described for the P3 pulse time. The possible range of the total count, Kc, during the P3 Period is 0Kc9. Thus all the S dip-flops must be considered during this period. Furthermore, as noted, during this period each external (high potential) input on Se or Sb corresponds to a decimal weight of two units. Because of this, the input equations to the vS1 ip-flop are automatically disposed of, since the S1 iiip-flop only changes with unit inputs, thus:

The S2 flip-flop, which manifests changes in counts of 2 units, will change its state to the opposite one with each single external input fed in during the P3 time. This is shown by equations:

Referring to Figure 8, vthe S3 flip-flop during the P3 time will change from a 0 to a 1 state when it is in a 0 state and at least two inputs are observed during this time each weighted as two units. l These two unit signals may consist of either a pair of external inputs', or the true state Iof the S2 flip-flop and one of the external inputs. Thus:

If two such two unit manifestations are present during a P3 time when the S3 flip-flop is already in a true state, the S3 ip-op is rendered false since the observed decimal count becomes 8 or 9 which, as seen in the table of Figure 8, is represented by a 0 in the C3 ipflop, hence:

os3=S3(SaSb-ISaS2-l-Sb$2)CPs As for the S4 flip-flop during the P3 time, using the same reasoning which renders the S3 flip-Hop false, if two two unit manifestations together with a true state of the S3 flip-flop are present during this period, the S4 flip-op is rendered tule by the equation:

On the other hand, the S4 flip-op is never rendered false during the P3 time since the count never exceeds decimal 9 hence:

The input to the S1 ip-op to render it false during the P4 pulse time will next be considered.

If during this time both S3 and S4 flip-,ops are false there is either a decimal 0, 1, 2 or 3 in the counting stages. Thus if either one or theother inputs is false, as designated by Se or Sb', while S3 and S4 are false, no carry occurs during P4 time and the S1 flip-flop is made false. It should be noted that when the counter has a decimal 4 therein, the S1 ip-op is already false and hence this is an exception which will not be provided for. The S1 flip-op is also made false whenever both external inputs are false. Symbolically this is Written as:

The S2 ip-op equations during the P4, time are not important in counting but the flip-flop is reset to a false condition thus:

Referring back to Figure 8 it is noted that decimal count 3 is defined by the logical product S1S2S3S4. As for decimal count 4, since tlip-op S3 is already in a t-rue state it can be omitted from the equation, the reasoning being that since it is already indicating a true state no provisions need be made for putting it in that state. The decimal 8 and` 9 terms are uniquely characterized by a true state of the S4 flip-flop. Hence, -the equation for defining fil whichcounts of the counter require afcomponent 2 in the output is:

It can be shown by examining the table in Figure 8 that'Si in the rst product is redundant, and as a result the a-bove equation can be further simpliliedas:

Looking at the conditions required to render the S3 flip-flop false, as noted in Table I of Figure 2, the weight 2 component output potential is low when the total count at P4 time, Kc, is equal to 0, 1, 2, 5, 6, or 7. Thus, the S3 iiip-lop which stores this weight 2 potential must be set into a false state.

Note that flip-flop S3 is already in a false state when Kc is equal to 0, 1, or 2; hence, the only requirements that must be met are those which will render ilip-op S3 false when Kc is equal to 5, 6, or 7. Referring to Figure 8, these latter contents are characterized by logical products S4S3SzS1, SiSaSzSi and S4S3S2S1, respectively. Term S4 can be omitted here since it is quite obvious that whenever the S3 ilip-op is true the S4 flip-flop must necessarily be false, i. e., according to the table in Figure 8, both flip-ops S3 and S4 cannot be true at the same time. Symbolically adding these products and noting that S3 is a common term in theseproducts, the equa` The equation canrbe further simplified to os3=S3(S1-i-S2)CP4 Referring to the S4 flip-flop, dur-ing the P4. time, it is desired to hold therein the weight 5 pulse, as the result of the counting, which is to be fed out later as a component of the coded sum. Thus, the S4 flip-dop is made true whenever the decimal sum output has the component 5 therein. Referring to Figure 2, it can be seen that this is true for an observed count of 5, 6, 7, 8, 9, 15, 16, 17, 18, `or 19 during this time.

Assuming rst that no inputs are evident on Se or Sb during the P4 time, if the counter contents is a decimal 5, 6, 7, 8 or 9, the S4 iiip-op is made true. Decimals 5 and 7 are observed in Figure S to be characterized by the product of terms S183; decimals 6 and 7 by product S253, and decimals 8 and 9 by the term Si. Combining these conditions the rst complex proposition (SiSs-i-SzSs-f-Sfi) is obtained for the s4 equation.

Assuming next that the inputs Sa and Se are taken into account, if neither or both of these inputs are present, the observed count includes the component 5 in the output and the S4 flip-Hop is to be rendered true. Thus, the second complex proposition (SaSb--SaSb), multiplying the rst, provides for both lthese possibilities.

Another manner of obtaining an observed count which will require a 5 component in the output is when the counter content during P4 time is 0, 1, 2, 3, or 4 and one, buttnot both, of the inputs Sa or Sb (weighted 5 units) is elfective. Anexpression which includes only these counts in the counter contents is S4(S1S2+Ss). The S4'S3 product is only true for the decimal contents through 3. The decimal 4 is characterized by the product S4S1S2. Adding these two products and factoring out the term S4 gives the desired expression. The introduction of one, butnot both, of the inputs Ss or Sa during this time is syrnbolically expressed by (SaSb-Sa'5b). Thus, collecting the above complex expressions, the equation for render-- ing the S4 flip-flop true during the P4 time is:

Referring nextto the triggering equation for rendering with the contents 0 through 4 in the counter, so as to give an observed count of 10 through 14, no change-need be made in the S4 iiip-tlopsince it is already in the zero state.

There is, however, onek set of lconditions which must be provided for rendering the S4v dip-flop false. This condition is when there is an input (high potential) on one or the other of the Sa or Sb inputs, and a content of 5 through 9 in the counter. The combined count is then in the range 1D through 14. As observed in Figure 8 for counter contents 5, 6 and 7 the S4"tlipilo'p is already O and, as before, this changeneed not be` provided for; but the 8 and 9 contents offthe'S counter demand that the S4 Hip-flop -be changed from a trueto a false state in order to indicate therein that no 5 Acomponent output is available.

The contents 8 and 9 are uniquely characterized by a 1 in the S4 ip-flop; as a result the equation for rendering the'S4 hip-flop false can be completely defined by the equation:

The logical equations for detining the output from the summer by means of the coded decimal representation will now be described. As was previously noted the corresponding weighted pulses in the output are delayed by two pulse times with respect Yto the input. As shown in Figure 1, the first potential period of the output is noted at P3 time. Thus, the decimal block of the output is evidenced at P3, P4, P1 and P2 ltimes for the components 1, l, 2 and 5, respectively.

Because of theA particular way in which the output representing the sumis used in computation, it is often desirable to generate aV waveform representingthe logical inverse of the true sum waveform. The reason for this is so that the output waveform generated can then be fed into an amplifier beforef applying it onto a memory such as a rotating magnetiewheel', for example. The amplifying device inverts the signal applied thereto, thus, giving the desired waveform at its output.

For this reason, the symbolic equation for the logical inverse of the binary coded output waveform is here presented, but it is to besrealized that this choice is arbitrary in that, if desired, the sum waveform could be obtained directly.

Thedecision as to whether or not a component is to be made effective in the output for a givencontent of the summer counter is determined by Table i in vFigure 2. The first component, weighted 1, is fed out of the summer during P3 time.

During this time the count KB can be observedin the counter and, if KB=O or 5 and there are no high incoming potentials at P3 time, there will be a zero output at this time, as noted by Table of Figure 2. Since it is the logical inverse of the sum which is desired, it is the obor 8 there will be a high potential at the output.

lso ifV the contents of the S counter is 3, and one but not both of the external inputs has a high potential, as noted by SiSzSaSbf -l- (SaSb) the observed count during the P3 time is equal to 5. i

Collecting all these conditions thelogical expression which represents the rst component of the output block, as observed during the P3 time, is:

During the P4 time the output potential from the summer, if high, indicates that the second component .l of the sum output is to be omitted.

Referring to Table I of Figure 2, if Kc=0, 1, 3, 5, 6,

Referring to Figure 8, the conditions of the S counter which evidence these counts are:

Taking counts and 8 together, it can be seen that these two terms can reduce to S3S2'S1 since (S4+S4)=1.

In a similar manner taking counts l and 3, it is made evident that these two termsv reduce to S4S3'S1 since (S2-|S2) 1.

As for counts and 6, it can be shown that the term S4 is redundant in these expressions because of the range of the counts which cannot exceed 9. An S4 term (8) along with an S3 term (4) would necessarily be out of the range of possibilities. Thus, the expression for the output during P4 time, is:

During the P1 time, the output indicative of the weight 2 potential is to be fed out of the summer circuit. Y

It was possible to determine whether this component i would appear in the output during the previous P4 timing pulse. At that time, the S3 flip-flop was made true if the lcomponent was to be represented in the output sum.

` Since the logical inverse of the sum is desired, when S3 is high there is no Weight 2 potential to `be fed out. This is indicated by S0'=F1'F2 S3' Finally during Pz time, the indication for the weight 5 potential is read out. This output was previously recorded in the S4 flip-op during P4 time. When`S4 is high there is no weight 5 output potential. This is indicated by:

So'=F1F2S4' Combining all these outputs the equation becomes:

Before presenting the physical circuits for generating the logical equations needed for the grid inputs to the S counter flip-ops, further simplification of the equations, as shown, is desirable.

The first step in this simpliiication is obtained by writing a single equation for the grid input to 'each of the iiipiiops. For example instead of having as many as four triggering equations, as in Figure 9, one for each of the timing pulses P1, P2, P3 and P4, respectively, a single equation can be written for the sr grid input. s1=S1(SaSb-tSaSb)CP1+S1(SaSbt-SaSb)CP2-I [(SiSs-i-SzSs-l-Si) (Sa-ISb){,SaSb]CP4 By substituting the F terms for the P timing pulses, and factoring out common terms this equation reduces to lt should be noted that (F1+F1)=,l and can be dropped;

out of the equation.

In a similar manner the overall osi equation can be shown to be equal to:

As for the S2 flip-dop grid equations, these may be collected to obtain the following:

The equation for the false grid of the S2 ip-op can be expressed by the overall equation:

Note in Figure 9 that the osz equation at P1 time is equal to O. However, it can be assumed that it is equal to without having any eect since the S2 lip-ilop is always set false after the previous P4 time, and consequently S2 can never be of high potential during the P1 time,

The only difference betwen the above expression and the cs2 equation for P2 time are the timing pulses themselves. As has already been described, by substituting the F `terms for the P1 and Pz timing pulses, the expressions reduce to the single term F2 because the F 1 flip-flop terms are shown to be superfluous.

Thus the underlined F1 term can be eliminated from the overall osz equation presented above.

The true grid equations of the S3 iiip-op can be combined to form the single equation:

`The false vgrid equations of the S3 ip-iiop are combined to form the single equation:

Thel true grid equations of the S4 flipflop can be written:

And the false grid equations of the S4 ip-flop can be written as:

To obtain the physical circuits for generating the logical equations needed for the grid inputs to the S counter flip-flops, it is noted that certain of the combinations of terms are used repeatedly in several equations. By generating each of these certain combinations once, a single derived proposition is available which can be introduced where needed with other terms to solve the various equations. In Figure 10, the logical nets for generating these combinations of terms are shown.

The typical logical addition is here introduced. This circuit, as shown by block 45 in Figure 10, is comprised in this case of a pair of input diodes 46 and 47 whose cathode-ends are joined and returned to ground through a common resistor R5. The input terms to the circuit are .fed in on the anode-ends of the diodes. Here, the

input t) represents the products SaSb as obtained from the first product circuit 51 and the input 52 represents the product SaSb as obtained from the second product circuit 53. When either one, or both, of the inputs to logical addition circuit 45 is relatively high in potential, output line S4 is raised to a relatively high potential in dicative of the logical sum (SaSe-i-SaSb'). Thus in general it can be stated that in a logical addition circuit, regardless of the number of inputs, the output potential equals the highest input potential.

It should be understood that the inputs Sa and Sb are here shown to be fed through inverters 55 and 56, respectively, so as to obtain their logical inverses Sa and Sb', which are needed as terms in the equations. The actual source of Sa and Sb could, however, be obtained from the false outputs ofv say, flip-flops Sa and'Sb, respectively, if such a source were used for the incoming coded digits.

The diode networks provided for solving the remaining combinations are comprised'of typical logical product' and logical sum circuits. In` each case, the outputli'ne is marked with a bracketed function Whichit represents.l

In Figures 11 through 17, the logical nets for physically solving the triggering equations for the S1, S2, S3 and S4 flip-flops are shown. ln each case, the logical equation for either the true or false grid is written belowthe net which, in effect, solves it. lt should be noted that the inputs to the nets defined by bracketed functions represent the complex terms already generated by the network in Figure 10. The output from the logicalnet, in each case, is obtained from a final logical product circuit which includes among other possible common terms, a clock pulse.

Inworder to simplify the logical nets, occasionally a term is introduced which multiplies one'of aplurality of complexcombinations which are being logically added together. This is permissible if the term introduced rep'- resents the opposite state of the flip-flop from that which the equation is to control. This makes it possible to factor out this term so that it need only be introduced once-in the final product circuit along with the clock pulse C. An example of this is in Figure 13 Where the term S2 (shown broken) was introduced into the last combination of the 052 equation. This term appeared in the previous two combinations which were to be symbolically` added to this last one.

Referring to the logical net for generating osz, it is noted that the S2 term is only introduced once in the final product circuit 55a.

This same change in the logical circuits is made in .Figuresv 14 and 15 which Igenerate the s3 and osx triggering equations, respectively.

ln Figure 18, the logical circuit for generating the logical inverse of the sum output waveform, So is presented. By feeding the So logical net output into an inverter 57, which may be an amplifier, for example, the desired waveform So can be obtained.

Here the output is not synchronized with a clock pulse, as was each of the grid equations, since the output is not being used to trigger a flip-flop.

This output wave can be fed, yfor example, into a memory or maybe observed by means of an oscillograph, depending on how the summer circuit fits into the re maining system of a computer.

Referring back to Figure 1, the operation of the summining circuit 10, upon receiving the coded digits there shown, will next be described in detail.

The contents of the Sl, S2, S3, and S4 flip-flops are all Zero initially, that is, they are all in their false states. Upon receipt of the unit inputsV (high potentials) present on Se and Sb during P1 ltime of the first cycle, the circuits are Vset up so as to trigger the S2 fiip-flop to a true state at the end of the P1 timing period. The counter now contains the decimal 2. During the P2 time of the first cyclegunit inputs are again shown to be present on both 16 Sa and Sb. As a result of this, at the end of the P2 period, the S2 flip-flop is caused to be made false and the S3 flip-flop to be made true, thus recording a decimal 4 in the counter. During the P3 time of the first cycle, the Sa potential is noted to be loW and the Sb potential to be high. Each high potential during this time represents a weight 2 component and as a result of receiving this single input the S2 ip-op is triggered true. Both the S2 and S3 flip-flops are now true, and as seen by Figure 8, this represents a decimal 6 content.

As previously mentioned, there is an inherent two clock pulse delay with which the summer emits binary digit outputs with respect to corresponding binary digit inputs. This delay is determined by the maximum number of additional input binary digits which must be observed in order to determine any of the output binary digits. ln the present system, in order to'determine the tirst output component of a digit, the first three input components must be observed.

Thus vduring P3, the first component of the output number weighted 1 can be determined by observing the counter contents and the inputs Sa and Sb. As previously described, when the total observed count during this time is 0 or 5, no output (low potential) is emitted. Conversely, an output (high potential) is emitted for any other count, which is the case of the present example. Hence, a high potential is fed from the summer during the P3 period.

During the P4 time the weight 5 components of the coded digits are received. As shown, only one of these, Sa, is received during the first cycle.

It should be noted that the inputs during the P4 time are neverrecorded as a count in the counter. At this point, since all the components of the incoming digits have been observed, all the remaining components of the outgoing digit can be determined.' Thus by noting what the total observed count is, the following decisions are made during the P4 time r firstly, the existence of the second'component of the output, weighted 1, is determined and fed out; secondly, the existence of the third component of the output, weighted 2, is determined and stored at the end of this time in the S3 flip-flop; thirdly, the existence of the fourth component of the output, weighted 5, is `determined and stored at the end of this time in the S4 :dip-flop; and fourthly, the decimal carry, if any, is determined and stored at the end of this time in the S1 flip-dop.

In the present example, `during the P4 time, the counter content 6 together with the observed input weighted 5 gave the decimal 11. This means a coded binary number (Figure 2) equivalent-to the decimal 1 is to be fed out and a decimal carry is to be added to the following incoming digits.

As shown in Figure 2, the second component of the outgoing coded Idigit representing decimal 1 is absent.

, Hence, inY accordance with the output logical net previously described, a low potential is fed out during the P4 time from the'surnmer. Likewise the third component weighted 2 is absent in the output. This fact results in the S3 flip-flop being triggered to a false state. Lastly, the weight 5 component is seen to be absent in the output and so the S4 fiip-op is triggered to a false state.

During P1 and P2 times of the next cycle of operation of the summer, while the S1 and S2 flip-flops are being used to count the first two component inputs of the next input coded digit, the weight 2 and weight 5 output components are fed out of the S3 and S4 flip-flops, respectively, in this case the potentials being low. As these components areA fed out,l the corresponding flip-hops are reset to a false state so that they can again be used for counting during the P3 time.

This completes one cycle of operation of the summer circuit showing how the first input digit 7 When added to the first input digit 4 gives the first output digit 1. The following input digits 1 and 6 on Se and Sb, respectively,

i, when fedthrough the counter, taking into account the 17 decimal carry, then feeds out the second output digit 8.

While the circuits as shown and described herein are admirably adapted to fulfill the objects and features of advantage previously enumerated as desirable, it is to be understood that the invention is not to be limited to the specific features shown but that the means and construction herein disclosed are susceptible of modification in form, proportion, and arrangement of parts Without departing from the principle involved or sacrificing any of its advantages, and the invention is therefore claimed in embodiments of various forms all coming Within the scope of the claims which follow.

What is claimed is; p

1. Aserial summer circuit comprising means for receiving a first and second incoming number formed of groups of serially disposed binary digits which represent digits of a decimal system, each of said groups composed of four digital positions each Weighted to correspond to components of the decimal digit, a source of clock pulses synchronized in time with said binary digits, means for counting said clock pulses for generating timing periods in repeated cycles corresponding to the position of the binary digits in a group, four bistable state circuits disposed so that each corresponds to successive stages of a binary counter, circuit means associated with said bistable state circuits for registering therein during three of said timing periods a binary count of said binary input digits in accordance with their Weight, output circuit means for feeding out starting at some intermediate timing period the output binary digits obtained by observing the count in said bistable state circuits and the received input binary digits, storing circuit means responsive to the contents of said bistable state circuits and the incoming binary digits during the remaining timing period for storing in the higher stages of said bistable state circuits at the end of said remaining timing period the output binary digits not yet fed out, and for storingin the first stage bistable state circuit a carry, and circuit means for feeding out said stored binary digits one at a time during following timing periods.

2. A serial summer circuit comprising means for receiving a irst and second incoming number formed of groups of serially disposed binary digits which represent decimal digits, each of said groups composed of four digital positions, each weighted to correspond to the decimal components l, l, 2, and 5, respectively; a source of clock pulses synchronized in time with said digital positions; means for` counting Said clock pulses for indicating in repeated cycles a first, second, third and fourth timing period related to said digital positions; four bistable state circuits disposed so that each corresponds to a stage of a binary counter, each of said bistable state circuits having a pair of outputs indicating the states thereof and a pair of input circuits for controlling the states thereof; a plurality of logical circuits each connecting the output circuits of said bistable state circuits and the summer receiving means to the inputs of said bistable state circuits in accordance With a predetermined arrangement, said logical circuits including, a counting circuit operating to register in the rst two of said bistable state circuits at the end of said first timing period and in the first three of said bistable state circuits at the end of said second timing period the accumulated binary count of the incoming binary digits weighted as units, and for registering -in all of said bistable state circuits at the end of said third timing period the accumulated binary count including the incoming binary digits weighted two units; a first output circuit operating during said third timing period `to feed out a first binary ydigit of a group representing the decimal digit of an outgoing number, and operating during said fourth timing period to feed out a second binary digit; a storing circuit operating during said` fourth timing period to store in the last two bistable Vstate circuits the third and fourth output binary digits, and to store in the first bistable state circuit a decimalcar'ry in `accordance with said accumulated binary count and the incoming binary digits weighted tive units; a first clearing circuit operating during said fourth timing period for clearing said second bistable state circuit; second output circuit operating during the rst and second timing periods, respectively,

`of the succeeding timing cycle to feed out said stored third and fourth binary digits; and a second clearing circuit operating during said rst and second timing periods, respectively, of the succeeding timing cycle to clear said third and fourth bistable state circuits.

`3. A summing circuit for generating an outgoing coded number which is the sum of a pair of incoming coded numbers comprising: a pair of input lines, each serially receiving binary signals representing one of said incoming numbers, a group of four binary signals on an input line representing each of the digits of said numbers, each of the binary signals in a group weighted to represent components of said coded digits; a plurality of bistable state circuits; a first circuit means associated with said bistable state circuits and successively responsive to the irst three binary signals in the groups representing the4 same order coded digits of the incoming numbers for registering information concerning their combined weight count; and a second circuit means associated with said bistable state circuit and responsive to said registered information and the last two binary signals in said groups for deriving a group of binary signals representing the same order coded digit of the outgoing number.

4. A summing circuit for generating an outgoing coded decimal number which is the sum of a pair of incoming coded decimal numbers, comprising: a pair of inputs, each of said inputs beingimpressed by groups of binary signals representing single digits of said incoming numbers, each `of the binary signals in a group weighted to representcomponents of said digits; a plu- Yrality of bistable state devices; a first circuit means serially responsive to. the binary signals on both said inputs for registering `in said bistable state devices a combined weight count of a portion of the binary signals in the incoming .groups representing the same order digits; an output; a second circuit means responsive to said weight count and the remaining binary signals in said incoming groups to derive a group of binary signals to be impressed on said output representing a digit having the corresponding order in said outgoing number and a third circuitmeans for storing some of the output binary signals in said bistable state devices prior to impressing them on said output. s

5. A summer circuit comprising: means for simultaneously receiving a pair of incoming coded decimal numbers formed of groups of serially disposed binary signals, each of said groups representing a decimal digit, each of the binary signals in a group weighted to correspond to components of the coded digits; a plurality of bistable state circuits;` a first circuit means associated with said bistable state circuits for registering therein information concerning the combined weight count of a portion of the incoming binary signals representing the same order coded digits of the numbers to be added; a second circuit means responsive to said weight count and the remaining incoming binary signals representing saidcoded digits to derive a group of binary signals representing a digit having a 'corresponding order in the outgoing number; a third circuit means for temporarily registering some Iof thel derived binary signals of'said outgoing group in said bistable state circuits; and a fourth circuit means for serially feeding out the binary signals of said outgoing group in order, whereby the binary signals of the succeeding pair of incoming binary coded digits areA being counted by said first circuit means and being registered in some of said bistable state circuits while some of the binary signals of said outgoing 19 coded digit are still beingstoredrl saidremaining bistable statelcircuits. y Y

6. Aserial summercircuitgcoinprisingz' means for receiving a first and second incoming number each formed of sets of vserially received binary signals whichIV represent decimal digits, each of said'set's 'comprised of four digital periods each weighted'toecorrespond to components of the decimal digit; meansfor registering at the end of each of 'said lirst three Vdigital periods an accumulated weight count of the binary signal inputs and manifesting said `count by binary signals; 'means for generating the first binary signalof an' output set representing' the decimal digit of the sum during-the third digital period in response to the accumulated count binary'signals and the incoming binarysignals; means for generating the second binary signal of said outputset during the fourth digitalperiod in response to the'accumulated countbinary signals `and the incoming binarysfignals; means for deter- Vming the remaining binary 'signals of said output set during said fourth digital period in response to the accumulated `count binary signals and the incoming binary signals and causing said remaining binary signals to'be .manifested as output binary signals' frornsaid registering means at the end of said fourth digital period; and means for generating said remaining binary signals of said output set in order during the first twol digital periods associated with the following incoming 'sets of' binary signals.

` 7. A cyclically operated summing circuit for generating an outgoing coded number corresponding to the sum of a pair of incoming coded numbers comprising: means for simultaneously receiving groups of serially disposed binary signals representing digits of a numbering system having aradiX greater than two, each of the binary signals in a group having a `positional weightcorresponding t components of the digits in said numbering system; a source `of clock pulses synchronized in time with said binary signals; means counting said clock pulses for cyclically generating timing signals 'corresponding to' the position of said binary signals in a group; a vplurality of bistable state circuits; a iirst circuit means controlled by said timing signals to respond'to said'incomingfbinary signals for registering in said bistablestate circuits during y,each cycle of said counting means information concerning'the accumulated weight' count of a portion of the binarysignals'in corresponding Vincoming groups; and a second circuit means controlled lby said timing signals to respond to saidgregistered information 'in said bistable state circuits and said incoming binary lsignals for generating a group of outgoing vrbinary signals representing a digit of the output lcoded number,`whereby saidoutgoing group of `binary signals is delayed with respectto said corresponding incoming kgroups of binary lsignals by" an Vinterval less :than a cycle .of saidcounting means.'

8. A serial summer circuit comprising: means lfor receiving on separate input lines a first and'second incoming number each formed of sets of four serially received binary signals representing a single Avdecimal digit, each of said sets comprised of four digital periods each weighted to correspond to components of a decimal digit; counting means having a plurality of count lines responsive to the binary signals on said summer input lines for `registering at the end of each of said rst three digital periods an accumulated weight count of the binary signal inputs and manifesting said count by binary signals on said count lines; a summer output line; means lfor generating on said summer output line during the third digital period the rst binary signal of a set Arepresenting the decimal digit of the sum in response to binary signals `Von said count lines and the incoming binary signals on said input lines; means for generating on said summer output line the second binary signal vof said output set during the fourth digital periodY in response to binary signals on said count lines and the incoming binary 'signalsfron said input lines; means for determining the third and' fourth I binary signals of said output set during said fourth digital `period in response to 4 binary 'signals on said count lines yperiods associated with the following incoming sets of binary signals in response to binary signals on said.certain count lines.

9. A serial summer circuit comprising: means for receiving a first and second incoming number formed of groups of seriallydisposed'binary signals which represent digits of a decimal system, each of said groups composed of four digital positions each weighted to correspond to componentsof the decimal digit; a source of clock pulses synchronized in time with said binary signals; means counting said clock pulses for generating vtiming signals in repeated cycles corresponding to 'the positions of lthe binary signals in a group; a plurality of bistable state circuits disposed so that each corresponds to successive stages of va binary counter; circuit means responsive to the count in said bistable state circuits and the incoming binary signals for registering in said bistable state circuits attheend of each of the first three timing signals a binary weight count of said binary input signals; a first output circuit means responsive to the count in said bistable state circuits and the incoming binary signals for feeding out during the third timing signal the first output binary signal; a second output circuit means responsive to the count in said bistable state circuits and the incoming binary signals for feeding out during the fourth timing signal lthe second output binary signal; storing circuit means responsive to the contents of said bistable state circuits andthe incoming binary signals during the period of the fourth timing signal for storing in the last two stagesv of said bistable state circuits at the end of said fourth timing signalthe last two output binary signals of the sum and for storing in the first stage bistable state circuit a carry signal; and circuit means for feeding out said stored binary signals one at a time during the periods of the following two timing signals.

l0.V A summing circuit for generating an outgoing coded decimal number which is the sum of a pair-of incoming coded decimal numbers comprising: a pair of inputs, each serially sensing binary signals representing said incoming numbers, a group of four binary signals on an input representing each `of the `decimal digits of said number, each ofthe binary signals in a group weighted to represent components of the decimal dig-it; 4a plurali-ty of bistable state circuits; a first circuit means for registering inform-ation in said bistable state circuits concerning the combined weight count of theiirst three binary signals in the groups representing the same order deci-mal digits ofthe incoming numbers; an output; a .second circuit means responsive tothe last two binary signals in said -groups and the registered information in said bistable state circuits for deriving af-group of binary signals to be fed on said output, said latter group representing the decimal digit of the outgoing number; and a third circuit vmeans for registering in said bistable state circuits the last two signals in the output group prior to impressing them onto said output.

yl1. A summing circuit `for generating an outgoing coded decimal number which is the sum of a pair of incoming coded decimal numbers, comprising: a pair-ofinp-uts, each receiving binary signals representing one ofgsaid incoming numbers, a'group of said binarysignalsl oneach input representing a decimal digit, each of the binary signals lin a group'weightedto represent components ofthe decimal digit; a plurality ,of bistable state devices; a first circuit meansassociated lwith said V.bistable'state devices for registering `thereinja combined weight clount' of a portion of the incoming binary signals representing the same order decimal dig-its of the incoming numbers; an output; a second circuit means responsive to said weight count and the remaining incoming bint-try signals representing said l same order digits to derive a g-roup of binary signals to be fed on said output, said latter group representing the a second circuit means controlled by said third and fourth timing signals and responsive to concurring signals on the decimal digit of the outgoing number; a third circuit l incoming lgroups of binary signals representing the next fhigher order decimal digits of the incoming numbers.

`12. A summing circuit for generating an outgoing coded decimal number corresponding to the sum of a pair of incoming coded decimal numbers comprising: means for simultaneously receiving a rst and second train of binary signals representing said iirst and second incoming numbers, respectively, a group of four binary signals on a train representing each of the decimal digits of said numbers; a timing circuit for generating four timing signals defining each of the four signalsin said groups according to a given code; a plurality of bistable state devices; a first circuit mean-s controlled by said rst, second, and third timing signals and responsive to concurring signals on the incoming trains for registering in said bistable state devices a combined count of the signals representing the same order decimal digits of said incoming numbers;

incoming trains and the information registered in said bistable state devices for generating on an outgoing train the rst and second binary signals of a group representing the sum decimal digit, and for storing the third and fourth binary signals of said latter group in said bistable state devices; and a third circuit means controlled by saidrst and second timing signals and responsive to t-he inform-ation registered in said bistable state devices for generating the third and fourth binary signals of the sum decimal digit on said outgoing train.

References Cited in the le of this patent UNITED STATES PATENTS 2,404,047 Flory Iuly 16, 1946 2,429,227 Herbst Oct. 21, 1947 2,634,052 lBloch Apr. 7, 1953 OTHER REFERENCES Progress Report (2) on the Edvac., Moore School of Electrical Engineering, University of Pennsylvania, June 30, 1946, declassied February 13, 1947, Oice Tech. Services, publication on February 13, 1953, pages 1-1-27, 1-1-27A, 1-1-28 and 1-1-29.

A Functional Description of the Edvac., University of Pennsylvania, November 1,1949; volume II, Figures 104- 3-LC3, 104-7L D-1, and 104-10 LD-6. 

